Automated line scan analysis to quantify biosensor activity at the cell edge.

Biosensors are valuable tools used to image the subcellular localization and kinetics of protein activity in living cells. Signaling at the edge of motile cells that regulates cell protrusion and retraction is important in many aspects of cell physiology, and frequently studied using biosensors. However, quantitation and interpretation is limited by the heterogeneity of this signaling behavior; automated analytical approaches are required to systematically extract large data sets from biosensor studies for statistical analysis. Here we describe an automated analysis to relate the velocity at specific points along the cell edge with biosensor activity in adjoining regions. Time series of biosensor images are processed to interpolate a smooth edge of the cell at each time point. Profiles of biosensor activity ('line scans') are then calculated along lines perpendicular to the cell edge. An energy minimization method is used to calculate a velocity associated with each line scan. Sorting line scans by the proximal velocity has generated novel biological insights, as exemplified by analysis of the Src merobody biosensor. With the large data sets that can be generated automatically by this program, conclusions can be drawn that are not apparent from qualitative or 'manual' quantitative techniques. Our 'LineScan' software includes a graphical user interface (GUI) to facilitate application in other studies. It is available at hahnlab.com and is exemplified here in a study using the RhoC FLARE biosensor.

Systems biology analysis of G protein and MAP kinase signaling in yeast.

Approximately a third of all drugs act by binding directly to cell surface receptors coupled to G proteins. Other drugs act indirectly on these same pathways, for example, by inhibiting neurotransmitter reuptake or by blocking the inactivation of intracellular second messengers. These drugs have revolutionized the treatment of human disease. However, the complexity of G protein signaling mechanisms has significantly hampered our ability to identify additional new drug targets. Moreover, today's molecular pharmacologists are accustomed to working on narrowly focused problems centered on a single protein or enzymatic process. Here we describe emerging efforts in yeast aimed at identifying proteins and processes that modulate the function of receptors, G proteins and MAP kinase effectors. The scope of these efforts is far more systematic, comprehensive and quantitative than anything attempted previously, and includes integrated approaches in genetics, proteomics and computational biology.

Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations.

Transcriptional regulation is an inherently noisy process. The origins of this stochastic behavior can be traced to the random transitions among the discrete chemical states of operators that control the transcription rate and to finite number fluctuations in the biochemical reactions for the synthesis and degradation of transcripts. We develop stochastic models to which these random reactions are intrinsic and a series of simpler models derived explicitly from the first as approximations in different parameter regimes. This innate stochasticity can have both a quantitative and qualitative impact on the behavior of gene-regulatory networks. We introduce a natural generalization of deterministic bifurcations for classification of stochastic systems and show that simple noisy genetic switches have rich bifurcation structures; among them, bifurcations driven solely by changing the rate of operator fluctuations even as the underlying deterministic system remains unchanged. We find stochastic bistability where the deterministic equations predict monostability and vice-versa. We derive and solve equations for the mean waiting times for spontaneous transitions between quasistable states in these switches.

A macroscopic description of biomolecular transport.

We present a general algorithm for computing the effective diffusion coefficient of a general class of biomolecular transport processes. The method can be applied to spatially discrete and continuous processes and takes into account the effects of thermal diffusion and chemical kinetics. To provide an illustration of the algorithm, the problem of protein translocation is considered.

Models of post-translational protein translocation.

Organellar Hsp-70 is required for post-translational translocation into the endoplasmic reticulum and mitochondria. The functional role played by Hsp-70 is unknown. However, two operating principles have been suggested. The power stroke model proposes that Hsp-70 undergoes a conformational change, which pulls the precursor protein through the translocation pore, whereas, in the Brownian ratchet model, the role of Hsp-70 is simply to block backsliding through the pore. A mathematical analysis of both mechanisms is presented and reveals that qualitative differences between the models occur in the behavior of the mean velocity and effective diffusion coefficient as a function of Hsp-70 concentration. An experimental method is proposed for measuring these two quantities that only relies on current experimental techniques.

Protein turbines. I: The bacterial flagellar motor.

The bacterial flagellar motor is driven by a flux of ions between the cytoplasm and the periplasmic lumen. Here we show how an electrostatic mechanism can convert this ion flux into a rotary torque. We demonstrate that, with reasonable parameters, the model can reproduce many of the experimental measurements.

First passage statistics of periodically driven models for neural dynamics.

The dynamics of two simple neuron models subjected to periodic stimuli is studied at the level of the first passage time probability density. The results from analytic treatments of these models are presented, and a discussion of the important properties displayed by these models is given. Specifically, both models possess resonans phenomena in the first passage probability distribution, arising from of the interplay of characteristic time-scales in the system.

Enhanced quantum fluctuations in a chaotic single mode ammonia laser.

A detailed study of the effects of quantum fluctuations in a chaotic single mode laser is presented. It has been well established that the linear noise approximation eventually becomes invalid for the case of chaotic dynamics. A more accurate description of the laser is achieved through use of nonlinear Langevin equations. Simple expressions for the time evolution of the phases of the electric field and polarization are derived. These expressions predict that chaotic dynamics will greatly enhance phase diffusion. This prediction is verified through numerical simulations. A quantitative method, for determining the amount of amplification of quantum noise by chaos is discussed. This method makes use of a metric introduced in symbolic dynamics. The fluctuations are shown to have been amplified by over two orders of magnitude, making them macroscopically visible.

Amplification of intrinsic fluctuations by the Lorenz equations.

Macroscopic systems (e.g., hydrodynamics, chemical reactions, electrical circuits, etc.) manifest intrinsic fluctuations of molecular and thermal origin. When the macroscopic dynamics is deterministically chaotic, the intrinsic fluctuations may become amplified by several orders of magnitude. Numerical studies of this phenomenon are presented in detail for the Lorenz model. Amplification to macroscopic scales is exhibited, and quantitative methods (binning and a difference-norm) are presented for measuring macroscopically subliminal amplification effects. In order to test the quality of the numerical results, noise induced chaos is studied around a deterministically nonchaotic state, where the scaling law relating the Lyapunov exponent to noise strength obtained for maps is confirmed for the Lorenz model, a system of ordinary differential equations.